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t=\frac{10}{9}\times 6
Multiply both sides by 6, the reciprocal of \frac{1}{6}.
t=\frac{10\times 6}{9}
Express \frac{10}{9}\times 6 as a single fraction.
t=\frac{60}{9}
Multiply 10 and 6 to get 60.
t=\frac{20}{3}
Reduce the fraction \frac{60}{9} to lowest terms by extracting and canceling out 3.